Question 420079
Find the equation for the line that passes through the point (4,-2), and that is perpendicular to the line with the equation 3/4x-3y=-3. 
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Find the slope of the given equation, put it in the slope/intercept form; y= mx+b
{{{3/4}}}x - 3y = -3
-3y = {{{-3/4}}}x - 3
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y has to be positive, multiply by -1
3y = {{{3/4}}}x + 3
divide eq by 3
y = {{{3/12}}}x + 1
Reduce fraction
y = {{{1/4}}}x + 1
:
the slope of the given equation: m1 = {{{1/4}}}
the slope relationship of perpendicular lines: m1*m2 = -1
Find m2
{{{1/4}}}*m2 = -1
multiply both sides by 4
m2 = -4 is the slope of line perpendicular to the given equation
:
use the point/slope form to find the perpendicular line: y - y1 = m(x - x1)
we have: x1 = 4, y1 = -2, m = -4
y - (-2) = -4(x - 4)
y + 2 = -4x + 16
 y = -4x + 16 - 2
y = -4x + 14, is the equation of the perpendicular line